Only possible if you are arriving into Heathrow on another flight. Take flight connections airside bus to T3 (if not already there), go through security then go to lounge. When done, locate the door to arrivals (may need to ask for escort) then take flight connections airside bus to T5 and go through security again. Should probably leave lounge 2 hours before scheduled T5 departure.

Only worth it if your scheduled transit time is 5+ hours. Also, not sure of the transit security situation nowadays but if there are queues at T3 transit security, you would be selfishly delaying genuine passengers transiting to T3.